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In the calculus of variations, the condition f_(y^')(x,y,y^'(x_-))=f_(y^')(x,y,y^'(x_+)) must hold at a corner (x,y) of a minimizing arc E_(12).

If f is a continuous real-valued function on [a,b] and if any epsilon>0 is given, then there exists a polynomial p on [a,b] such that |f(x)-P(x)|<epsilon for all x in [a,b]. ...

Given a succession of nonsingular points which are on a nonhyperelliptic curve of curve genus p, but are not a group of the canonical series, the number of groups of the ...

A function, continuous in a finite closed interval, can be approximated with a preassigned accuracy by polynomials. A function of a real variable which is continuous and has ...

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

A nonconformal, equal-area projection which is a special case of the Bonne projection where one of the poles is taken as the standard parallel. Because of its heart shape, ...

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

The width of a box is the horizontal distance from side to side (usually defined to be greater than the depth, the horizontal distance from front to back).